ASTR 670: The ISM and gas dynamics
ASTR 670 is a PhD-level class that is split 50-50 between hydrodynamics and the interstellar medium (ISM). If those two topics sound like a lot of material for one course, they are! Given the time limitations, we focus on key aspects of each topic and leave numerous details aside (see the sample syllabus). Contrary to the course title, hydrodynamics is taught first because it is a prerequisite for a number of discussions in the ISM section.
The hydrodynamics part of the course begins by making the connection between the microphysics of particles and fluid quantities such as pressure and energy. We intuitively derive the Euler equations that govern inviscid hydrodynamics and apply them to some classic problems such as waves, instabilities, and shocks. We finish with a brief exploration of magneto-hydrodynamics (MHD). This part of the course relies on a detailed set of hydrodynamics notes.
In contrast with the mathematical hierarchy of problems and equations in hydrodynamics, the ISM constitutes a much more diffuse collection of topics. Interstellar gas comes in many different ionization states, temperatures, and densities, which means that countless physical processes are important for the state and evolution of the ISM. This section of the course is roughly organized by gas phase and tries to tie the most important microphysical processes (such as excitation and ionization) to the resulting astrophysical observations. Besides detailed ISM notes, we heavily rely on the excellent book by Draine as well as on lecture slides.
One important focus of the course as a whole is on numerical methods and practical applications, including coding-based homework sets and an applied semester project. A significant portion of the hydrodynamics part is devoted to the computational algorithms that are used to solve hydro problems in contemporary astrophysics. Much of this discussion is encapsulated in Ulula, an ultra-lightweight python hydro code for teaching and experimentation.